Jiyang, Shandong.

Mr. Zhou sorted out his books again, and his book boy was two years older.

"Sir, are we going to the capital this time?"

The scholar has become a disciple of Mr. Zhou.

Mr. Zhou has been to Beiping, has been received by the original Yan Shizi, and has been praised by the little prince himself as a great talent.

The Department of Science and Technology was registered and received a talent allowance.

The allowance is nothing for a large family, but if it is an ordinary person who has no source of livelihood, it can solve the problem of food and clothing.

"Hmm."

Mr. Zhou nodded.

The mathematicians in Beijing have proposed a new definition of symbols, how can such a mathematical festival be without themselves.

At this time.

Mr. Zhou's father stopped him.

"Recently, the capital has not been peaceful, and there may be a big case involved, so it's better to wait for the limelight to pass, and then you can go to the capital."

The old man's face showed concern.

Someone dared to plot to assassinate the saint, and when the news spread, it caused an uproar, and everyone was horrified.

The heinous act of rebellion, I don't know how many people will be implicated.

Even the recent social atmosphere in Shandong has become serious, and I don't know what the situation in the capital is, the old man comforted.

"We are academics, not in politics."

Mr. Zhou said indifferently.

Even if they don't do anything, they will not worry about their livelihood and will have more political privileges.

The government cannot govern them, and even if they commit crimes, the local government has no right to punish them, and the interrogation must involve the Department of Science and Technology.

No torture, no torture, separate place of detention, ensure a good environment, and have no worries about food and clothing.

Previously, their political privileges were limited to Beiping, and then extended to the north, and now Yan Shizi has become the emperor's grandson, and their privileges have also expanded to the entire Ming Dynasty.

It felt like overnight.

After being recognized by the Department of Science and Technology, the scholars who receive the talent allowance of the Department of Science and Technology have become the most comfortable group.

The old man felt helpless when he saw his son so simple.

Mr. Zhou was unwilling to miss the opportunity, so he took his scholar disciples, and the two took a train in Shandong and arrived in the capital on the third day.

At the beginning, Peking attracted many scholars from other places.

In the Hongwu Dynasty of the Ming Dynasty, the literary style flourished in the south, and under the prosperity of the literary style, there were only scholars who were interested in studying all kinds of knowledge in the soil, and there were not many scholars in Beiping.

The Jianghuai region is the place where the most scholars are located, most of them have returned to their hometowns, also received allowances, and have privileges in the capital, and scholars have flocked to the capital.

Mr. Zhou didn't expect that his father's reminder was right.

The banks of the Jianghuai River in the Jianghuai area are empty, and there is no luxury and beauty that friends say, only lonely flower boats.

But what's the matter with him?

He didn't care.

Several mathematicians were in the home of one of them, using the method of counting chips.

Arithmetic is the way in which Chinese numerical abbreviation is written.

It's very simple and scientific.

The smoothness and simplicity of numeral writing in ancient India are about the same level, but more comprehensive.

The vertical type is used for the single digit, the horizontal type is used for the ten digits, the vertical type is used for the hundreds, the horizontal type is used for the thousand digits, the vertical type is used for the 10,000 digits, and so on.

In this way, from right to left, vertical and horizontal, and so on, you can use arithmetic chips to represent arbitrarily large natural numbers.

Because of the vertical and horizontal transformation between bits, and the fixed way of writing each bit, it will neither be confused nor misplaced.

There is no doubt that such an arithmetic notation is completely consistent with the modern decimal notation.

"In the Eastern Han Dynasty's "Shuowen Jie Zi", it is recorded that rice weighs one, is twenty buckets of millet, and ten buckets of rice, which is called Yu; For the rice six buckets too half a bucket, said Zong. ”

A mathematician speaks as he describes it in the way of arithmetic.

"Rice is written as twenty, 毇 is written as ten, and rice is written as six and two-thirds."

"Twenty to ten to six and two-thirds."

(Because the writing method of arithmetic chips is not included in the input method, it can only be replaced by words, which is also the price of backwardness.) ）

Then the mathematician wrote another set of numbers.

"Sixty to thirty to twenty."

The mathematician wrote two equal words between two sets of numbers.

In ancient times, there was no equal symbol, and when it was written, it was represented by the Chinese character "etc" or "equal to".

"=" sign.

When it first appeared, it did not mean equal, and the French mathematician Vyette said in his work that "=" was used to add two quantities.

There is no clear definition of these messy symbols, just everyone's writing habits.

For example, some people use "" to represent equals, some people use the letter equivalent to pha as equals, and some people use one to represent equals.

Finally, because the works of the French mathematician Weida in the sixteenth century were widely disseminated, the "=" he used to use was known to more people, and it gradually became a tacit understanding, and even recognized as an equal sign by later generations.

Now a mathematician of the Ming Dynasty, he casually drew an apostrophe on the tail of a slash, and several people knew that it meant equal.

The more Mr. Zhou looked, the more fascinated he became.

"Do you understand this equation?"

"Isn't this the primary equation, and the more profound is Mr. Zhu Shijie's eternal equation, you can't bully us and be lonely and unheard." Mr. Zhou was dissatisfied with the other party's teasing.

The man smiled sheepishly.

Mr. Zhou's Zhu Shijie is a Han Chinese, born in the south when the Southern Song Dynasty fell, he traveled around the south and exchanged knowledge with mathematicians in the south, which was later called Zhu Shijie's identity equation.

Several mathematicians quickly negotiated a set of symbols.

The words equal, multiply, divide, divide, and so on, are marked with detailed concepts and accompanied by symbols they draw.

In the journal Mathematics, their results were published.

This issue of the journal of mathematics has aroused the dissatisfaction of many mathematicians.

"Why did a few of them define a symbol and why do they use his symbol?" Another scholar complained to the Technical Newspaper and asked the Technical Journal to retract the manuscript.

Many scholars have complained.

This article of the Technology Newspaper caused an earthquake in the academic community.

It is incomprehensible inside and outside the capital.

Cabinet.

Huang Huai said incredulously: "People now dare not come out for fear of being implicated, why don't they care." ”

"His Royal Highness the Emperor Sun treats scholars best, they stay out of the matter, what is there to care about."

Xie Jin understands.

"Isn't it just a symbol, I think they want to fight."

"Haha."

Xie Jin couldn't help but smile and said: "This is a battle for the right to speak, let alone quarrels, even if someone fights, I'm not surprised." ”

Say what you say, and it's coming.

The day after Xie Jincai finished speaking, two scholars really fought on the streets of the capital.

alarmed the inspector Ding Cha, they could only separate the two, and the first lesson of their training was the privilege of the scholars.

They have no authority to deal with academics, and can only ask academics if they are held accountable.

If you want to be held accountable, you have to ask the officials of the Department of Science and Technology to come forward, and the regulations are cumbersome, energy-consuming, and time-consuming.

The two scholars glared at each other, neither pursuing the other.

Mr. Zhou's actions have opened another door and aroused the interest of scholars in formulating definitions.

It's not a difficult thing to get published in a technical newspaper, gain fame, and leave your name in history.

Who doesn't rush to do it.

The hand is fast, the hand is slow.

Mr. Zhou came to the capital, of course, he will not return empty-handed, "Encyclopedia of Mathematical Symbols" is jointly published by several people, and it does not show his ability.

If it weren't for the fact that the library in the capital didn't provide accommodation, he would even have to live here.

After a while.

Zhu Gaochi heard that the officials of the Ministry of Rites had arranged for Zhu Di to greet him, approved and agreed, and in his spare time, he read today's newspaper.

The old rule, read the technical newspaper first.

"During the Shang Dynasty, the ancestor Mr. Shang Gao, the greatest mathematician in the world at that time, invented the Pythagorean theory and completed the proof."

"The development of agricultural technology in our Chinese civilization is unparalleled in the world, and agriculture is inseparable from astronomy, and astronomy is inseparable from mathematics and physics."

"As early as the Shang Dynasty, astronomical observation and astronomical surveys were made in ancient times, and the calendar was established, proposing that there are no steps to climb the sky, and the earth cannot be measured by size, how did the number come about?"

"Mr. Shang Gao, the ancestor of the people, put forward his moment theory, the number is obtained according to the principle of circle and square, the circle comes from the square, and the square comes from the moment."

"Moments are calculated from multiplication and division."

The "moment" proposed by Mr. Shang Gao originally referred to the Pythagorean measurement, a drawing tool containing right angles, and was analyzed with an example of 3:4:5 to complete the proof. ”

"In the process of proof, the use of the moment is also pointed out, the flat moment is the positive rope, the Yan moment is the hope height, the covering moment is the sound, the horizontal moment is the distance, the ring moment is the circle, and the closing moment is the square."

Zhu Gaochi looked a little struggling.

It was as if long-dead memories were attacking him.

"After the Shang Dynasty and the Zhou Dynasty, people needed a more accurate way of calculating, and Mr. Rongfang raised the difficult problem of how to calculate the diameter of the sun and the distance between the sun and the earth."

"Mr. Chen Zi, the ancestor of the Zhou Dynasty, has completed the proof."

"He proposed to use a hollow bamboo pole eight feet long (note: one foot at that time was equal to 0 six-nine feet today) to aim at the sun, and then at one end of the pole it was observed that the sun just covered the middle hole at the other end of the pole, so as to obtain the distance from the sun to the observation point on the ground/solar diameter = bamboo pole length / aperture = eighty:one."

In addition, the eight-foot-long bamboo pole was erected on an open space in the city of King Zhou, as a "table", also known as "hip"; It can be observed that at noon on the summer solstice every year, the shadow of the watch is the shortest, one foot six inches, and in the direction of due south and north, every thousand miles, the shadow is one inch shorter. ”

"So at noon on the day when the shadow was six feet long, there was no shadow of the sun sixty thousand miles south of the watch; Using the Pythagorean theorem and the proportional method, it was calculated that the distance between the sun and the shadowless place under the sun on the ground was 80,000 li, and the distance between the sun and the observation point of the royal city was 100,000 li, and the diameter of the sun was further calculated to be 1,250 li.

After reading it, Zhu Gaochi read it.

I couldn't help but laugh.

The average distance from the Sun to the Earth is 14,960 kilometers, and the diameter of the Sun is 1,390,000 kilometers.

So the ratio of the distance between the sun and the earth to the diameter of the sun is about one hundred and seven to one.

The result here is wrong.

It was not the formula that was wrong, but the ancients of the Zhou Dynasty, who believed that the earth was flat, so despite the correct mathematical principles, the error in their calculations was still very large.

Among them, the theory of right triangles, the Pythagorean theorem of three strands and four strings, was proposed and proved by Pythagoras in ancient Greece in the sixth century BC in the West, a full thousand years earlier.

If someone says that there is no geometry in ancient China, they can shoot him directly in the face, which is more than a thousand years earlier than the "Geometric Original".

The Western "Geometric Original" came out in 300 BC, but it was soon completely lost, unlike the Chinese "Zhou Ji Sutra" and "Nine Chapters of Arithmetic", which were passed down from generation to generation.

Of course.

The content in the later "Geometric Original" is great, but no one knows what is said in the original "Geometric Original", which is already a historical secret.

"Shang Gao, an ancestor mathematician of the Shang Dynasty, invented the Pythagorean theorem, the square of a right triangle, and the theory of square area, and put forward the concepts of moment, circle, and square."

1600 BC to 1046 BC.

"Chen Zi, an ancestor mathematician of the Zhou Dynasty, perfected the Pythagorean theorem and had a mature formula."

1046 BC to 256 BC.

"In the Jin Dynasty, the squares of each figure were solved, the equations were solved, and even Sun Tzu's theorem was born."

Zhu Gaochi couldn't understand it.

The large text records above, converted into the writing methods of later generations, Zhu Gaochi can recognize every word, but he does not know them together.

The meaning of the content is that for a set of integers Z, each number in Z is divided by the same number m, and the remainder can be 0, 1, 2, .m-1, a total of m types. Then, the size of the remainder is used as a criterion to divide Z into m classes. Each class has the same remainder.

According to the equation, it is:

Let b (x) be the polynomial of integer coefficients, then the congruence equation f(x) = 0 (mod m) is equivalent to f(x) + b(x) = b(x) (mod m);

Let b be an integer and (b,m) = 1, then the congruence equation f(x) = 0 (mod m) is equivalent to bf(x) = 0 (mod m);

Let m be a prime number, f(x)=g(x)h(x), g(x) and h (x) are integer coefficient polynomials, and xo is the solution of the same spinning range f(x)= 0 (mod m), then xo must be the solution of the congruence equation g(x)= 0 (mod m) or h(x)= 0(mod m).

Proof that: (1) if f(xo) = 0(modm), then f(xo) + b(xo) = b(xo)(mod m) is true, and conversely, if f(xo) + b(xo) = b(x0)(mod m), then f(xo) = 0(mod m) is true;

(2) If f(xo) = 0(mod m), then bf(xo) = 0(mod m) is true, and conversely, if bf(xo) = 0(mod m), then f(xo) = 0(modm) is true from (b, m) = 1;

(3) If g(xo)h (xo) = 0 (mod m), then g (xo) = 0 (mod m) or h (xo) = 0 (mod m) is given by m being prime. Certification.

The math problems of the Shang Dynasty and the Zhou Dynasty, Zhu Gaochi can still do it, and he can see the meaning.

When it came to the Northern and Southern Dynasties, Zhu Gaochi would no longer do it.

"Mathematics is always the smartest people who can play and understand it, no matter what era it is." Zhu Gaochi muttered, giving up the act of competing with himself.

"Mr. Yang Hui, a mathematician in the Southern Song Dynasty, invented the geometric arrangement of Yang Hui's triangle, and the coefficients that expand on Sun Tzu's theorem, for example, in Yang Hui's triangle, the three numbers in the third row correspond exactly to the coefficients of each term of the expansion formula of the sum of two numbers, and the four numbers in the fourth row correspond to the coefficients of each term of the expansion formula of the sum of two numbers, and so on."

……

Zhu Gaochi didn't look at it.

It's really a headache to see, in short, the famous scholar surnamed Zhou he met in Peking sorted out the mathematics and physics of the past dynasties, and unlike others, he carried out formulas and symbols.

And each theory, theorem, equation, etc., is given a label and origin, forming a complete system.

For example, in the Shang Dynasty, people's knowledge was limited, so they formed a trigonometric algorithm, and then with the development of civilization, by the time of the Zhou Dynasty, people not only had an algorithm of triangular area, but also formed a formula.

In the Han Dynasty, the mathematician Liu Hui wrote "Nine Chapters of Arithmetic" during the Three Kingdoms period, in which the height of the island was calculated through the naked eye and tools, and various advanced mathematics.

Then there was the Jin Dynasty, with more complex equation algorithms, and when it came to the Southern Song Dynasty, mathematics and physics were pushed to a climax.

After the fall of the Southern Song Dynasty and the beginning of the Yuan Dynasty, Zhu Shijie, the world's greatest mathematician at that time, summarized and optimized China's mathematics and physics, and promoted it to an unprecedented height.

It even studied the essence of mathematics and formed the concept of spatial situation and quantitative relations.

Zhu Gaochi was very happy.

even almost forgot to greet Zhu Di.

The importance of mathematics is very important, both ancient and modern.

Not to mention the technology of the rest of the industries, only where did the excellent agricultural technology of ancient times come from? Did it fall from the sky?

A developed agricultural society is inseparable from a high degree of awareness of celestial phenomena.

The excellent calendar allowed the ancient farmers to clearly know how to farm, which needed the support of science and technology, rather than being thought up randomly.

Nowadays, with a more complete mathematical system, the technological development of industrialization has a solid support.

How can Zhu Gaochi alone promote the whole society.

He relied on the developed scientific and technological civilization of ancient China.

"For scholars, we must pay the greatest attention." Zhu Gaochi said in the cabinet and asked the cabinet to discuss the law.

He wanted to make laws that would protect the social status of scholars and provide them with an adequate environment.

No one can suppress academics.

Any scholar.

As long as he passes the assessment of the Department of Science and Technology, he can have no worries about food and clothing, even if he has not researched a single result.

It's the same as the ancient emphasis on readers.

Zhu Gaochi just pointed out the group of people he valued.

Scholar.

From the reader.

Again, it didn't come out of nowhere.

There is something going on in the company today, and there may only be one chapter, which is a big chapter, nearly 5,000 words, so send it out first, and if you have time in the evening, try to write another chapter.

(End of chapter)